...Antranik A. Siranosian; Miroslav Krstic; Andrey Smyshlyaev; Matt Bement We present a control design method for nonlinear partial differential equations (PDEs) based on a combination of gain scheduling and backstepping theory for linear PDEs. A benchmark first-order hyperbolic system...

...Miroslav Krstic Smith predictorlike designs for compensation of arbitrarily long input delays are commonly available only for finite-dimensional systems. Only very few examples exist, where such compensation has been achieved for partial differential equation (PDE) systems, including our recent...

... on their analyses. The numeric model is a partial differential equation based model approximated by difference equations, including both channels and both GDLs of a PEMFC. The reduced model uses a semi-analytic solution method, which is a combination of analytic and numeric solutions, gaining physical intuition...

... equations using Pontryagin’s minimum principle or the Hamilton–Jacobi–Bellman partial differential equation using dynamic programming in one unified framework. In addition, the differential transformation algorithm can efficiently solve optimal control problems with the piecewise continuous dynamics...

... of the beam using only actuation at the base. The explicit deflection angle reference solution is found as a result of writing the shear beam model in a strict-feedback form. Special “partial differential equation (PDE) backstepping” transformations relate the strict-feedback model to a “target system...

... and reaction process. Modeling the spatio-temporal dynamics of this metallurgical process, however, requires partial differential equations that are cumbersome to solve on-line, as part of a real time reference model to the controller. To this end, we present a computationally parallel and meshless model (i.e...

...Nhan Nguyen; Mark Ardema This paper is concerned with optimal control of a class of distributed-parameter systems governed by first-order, quasilinear hyperbolic partial differential equations that arise in optimal control problems of many physical systems such as fluids dynamics and elastodynamics...

...Blaise A. Horban; Eric P. Fahrenthold Conventional models of high velocity impact dynamics rely on approximate solutions of the governing partial differential equations for an elastic-plastic continuum, developed using weighted residual, finite difference, or other techniques prevalent...

... presents an algorithm for the conversion of a class of nonlinear systems with two inputs to a high-order chained, or generalized chained, form. The feedback transformation accomplishing this conversion is derived, provided certain conditions hold, by solving a system of partial differential equations...

... nonlinear dynamical systems dynamics nonlinear control systems partial differential equations integro-differential equations damping fibre optic sensors state-space methods frequency response position control tracking At the University of Washington’s Human Interface Technology Lab, small...

... model, respectively, are shown in Fig. 2 , together with the iteration numbers required in the projected gradient method and the converged values of the objective function J . For the brevity of communication, we call the method employing the original partial differential equation the SM-CG, while...

... end to a rotating hinge point at the other end. Basic models for friction and beam dissipation effects are included. A nonlinear integro-partial differential equation is derived for the complete beam/mass system in the curved space of the deformed beam. The resulting equation is cast...

... partial differential equations, the separation being allowed by a two time scale analysis of the system. The model has been identified, through a purposely designed genetic algorithm, and validated on experimental data. Contributed by the Dynamic Systems and Control Division for publication...

... transient dynamic equations for hydraulic dynamic studies. The fundamental equations are a pair of quasi-linear hyperbolic partial differential equations expressed as follows: (1) 1 ρ ∂ P ∂ t + V   ∂ P ∂ x + a 2   ∂ V ∂ x = 0...

...H. M. Park; O. Y. Kim The Karhunen–Loe`ve Galerkin procedure (Park, H. M., and Cho, D. H., 1996, “Low Dimensional Modeling of Flow Reactors,” Int. J. Heat Mass Transf., 39 , pp. 3311–3323) is a type of reduction method that can be used to solve linear or nonlinear partial differential equations...

... γ i h i x ] ad E 0 k − λ − j − 1 E ¯ x ] = 0 , for i ∈ J p and k ∈ J 2 n It is remarked that ( 3.11b ) and ( 3.11c ) constitute a system of first order partial differential equations with respect to a i x...